Proposition XIII.2 — If the square on a straight line be five times the square on…

Proof

Converse of XIII.1: assume the squared relation and deduce the extreme-and-mean cut using II.6 / II.11.

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Full neighborhood

Depends on (3)

II.6Proposition II.6If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the…
II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…
XIII.1Proposition XIII.1If a straight line be cut in extreme and mean ratio, the square on the greater segment added to the half of the whole…

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